3 main points that i really took attention to:
1) kanade's favorite food is mapo tofu, which is so spicy no one will ever eat it. but once u eat it, u realize it's actually good. it is in comparison to kanade's personality. no one in SSS wants to try to be friends with her, but she's actually a sweet considerate person. otonashi is the first one to try mapo tofu, and the first person to try to become friends with kanade.
2) otonashi, from his past, realized that he only wished to live to become a doctor so that he will hear a lot of 'thank you' from other people. However, in the other world, the fact that if kanade's feelings were heard (her telling him thank you for the heart donation and giving her life), then she would dissapear. that is what otonashi didn't want. this is almost a contradiction: otonashi wants people to thank him, but he doesn't want kanade to thank him because he loves her and he wants her to stay. ultimately, he gives up his own feelings and desires and grants kanade the freedom to dissapear from that world and earn a peaceful departure in the afterlife.
3) in the scene where the leader goes to the computer room underground (when ppl were turning into NPC's), she has a conversation with the dude there. After watching it 3 times, I finally understood what it meant. The guy, who at the present, is an NPC, was an actual person long ago. He, like otonashi, wandered into this world even though he did not have regrets upon death. Naturally, he also lost his memories. However, just like otonashi, he fell in love with a girl in this world. When people fall in love, they desire constance. He wished the girl would not disappear, even after her wishes has been granted and her regrets relieved. However, she did. And the guy still remained. The reasoning is this: The world was meant so that people are to eventually dissappear, or 'graduate' after their regrets have been relieved. However, if people start falling in love, they don't want to put an end to the life in that world and want to stay forever. That is almost like cheating life. Because in that world, you never age, time stays the same. Therefore this cannot be allowed. Even so, the guy stayed in the world believing that there would come a time when that girl would revisit this world and he could see her again. Waiting perhaps over a thousand years or so, his mind became crazy and his heart lovesick, that he became insane and became an NPC himself. This concept is REALLY important because it is a crucial symbolism to otonashi's state of being. He also wandered into this world losing his memories, even tho he did not have any regrets. But here is the difference: because otonashi died, and he doesn't know what happened to his organs after his death, he doesn't know if that heart delivered to someone and saved someone's life. But the key point is that he finds out at the end, that because he helped kanade live, he had no regrets dying. However, because at the last scene, kanade is going to dissappear, his newly found regret is formed in this world, not his past life. This is the most interesting part. His regrets do not lie in his past real life, but it lies in the current world, as kanade dissapears. What happens to otonashi after? does he stay in this world and await kanade's return just as the other NPC did? no one knows. this is the uncertainty of the anime.
tl;dr version
Angel Beats is an AMAZING anime. Though it lacks character development for the most part, the story is WELL-THOUGHT OUT, and the fantasy-like romance that is developed throughout the anime is one of a kind. This is an anime that everyone should watch, regardless of whether they like anime or not in general.